Question

The net weight on a box of cereal says 14.5 ounces. However, the factory considers any box within 0.25 ounces acceptable to sell
Part 1:
Identify the inequality that represents the scenario described above
Part 2: Solve the inequality from Part 1. Include all your work in your solution
Part 3: Explain what your answer means in the context of this problem

Answer 1

Part 1 — inequality:
|x − 14.5| ≤ 0.25

(Here x is the box's net weight in ounces; "within 0.25 ounces" means the distance from 14.5 is at most 0.25.)

Part 2 — solve:
|x − 14.5| ≤ 0.25
is equivalent to
−0.25 ≤ x − 14.5 ≤ 0.25
add 14.5 to each part:
14.5 − 0.25 ≤ x ≤ 14.5 + 0.25
14.25 ≤ x ≤ 14.75

Part 3 — interpretation:
Any cereal box with net weight between 14.25 ounces and 14.75 ounces (inclusive) is considered acceptable to sell. Boxes under 14.25 oz are too light and boxes over 14.75 oz exceed the allowed deviation.